Update...
While allowing the twice-steam-cleaned carpet to dry, I had the cats' old litterbox in the hallway next to the bedroom entrance. About 15 minutes ago, I heard the stupid cat in the bedroom, wailing.
I entered the room, and it was clear that he was searching for the litterbox, so I picked him and placed him right in front of the litterbox in the hallway. He re-entered the bedroom.
So I began to prepare one of the two litterboxes. Before I had finished, I peeked back into the bedroom to find another felinoid fecal assault in progress, about one foot to the left of one of the formerly heavily stained areas.
Because I caught him in the act, I entered the room, slammed the door shut, shoved his face up to the poo pile and yelled at him. Is it mean? Probably, but in the last two days, I've spent over $300 for a new steam cleaner, new chemicals, two new litterboxes, and a truckload or three of cat litter, and I've spent valuable time that could have been spent working on MBA studies in order to cater to this stupid shit machine.
I've put one of the new litterboxes in the corner of the room formerly occupied by the old litterbox, even though the carpet is still damp. I'm reassembling the air-drying components of the steam cleaner to go over the newly defiled region of the room for the third time today. Then I'll put the second litterbox near where he just crapped.
I don't know what else to do.